Page:Calculus Made Easy.pdf/45

Summary. Let us see how far we have got. We have arrived at the following rule: To differentiate $x^{n}$, multiply by the power and reduce the power by one, so giving us $nx^{n-1}$ as the result.

 

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Exercises I. (See p. 254 for Answers.)

Differentiate the following:

(1) $y=x^{13}$	(2) $y=x^{\tfrac {-3}{2}}$
(3) $y=x^{2a}$	(4) $u=t^{2\cdot 4}$
(5) $z={\sqrt[{3}]{u}}$	(6) $y={\sqrt[{3}]{x^{-5}}}$
(7) $u={\sqrt[{5}]{\tfrac {1}{x^{8}}}}$	(8) $y=2x^{a}$
(9) $y={\sqrt[{q}]{x^{3}}}$	(10) $y={\sqrt[{n}]{\tfrac {1}{x^{m}}}}$

You have now learned how to differentiate powers of $x$. How easy it is!